Course for Molecular Modelling Elementary Principles and Applications Jian Wan Department of Chemistry Central China Normal University Wuhan 430079, China Tel: +86-27-6786-2022 E-mail: jianwan@mail.ccnu.edu.cn
Molecular Modelling
Outline 1. The Theoretical Background Gaussian98/GaussView 2. Single Point Energy Calculations 3. Geometry Optimizations 4. Frequency Calculations 5. Reaction Pathways
References Exploring Chemistry with Electronic Structure Methods, J. R. Fores man, A. Frisch, Second Edition Gaussian, Inc. Molecular Modelling, A. R. Leach, Addison Wesley Long-man Limit ed, 1996. www.gaussian.com
Chapter One The Theoretical Background
1.1 Molecular Modelling (Computational Chemistry ) Molecular Modelling 1. Molecular Mechanics (MM ) 2. Molecular Dynamics (MD ) 3. Electronic Structure Theory ( ) Quantum Mechanics, QC & Semiempirical QC (Ab initio Methods) 4. Quantum Statistics ( )
1 2 3 (local minimum)
1.1.1 Molecular Mechanics Advantages Disadvantages
.1.2 Electronic Structure Theory a) Semi-empirical QC Methods HMO AM1 MNDO PM3 INDO/S b) Ab initio Hartree-Fock c) Density Functional Theory DFT/B3LYP DFT/X3LYP Gaussian MOPAC HyperChem
homework Functions in Gaussian98 Molecular energy and structures Energies and structures of transition states Bond and reaction energies Molecular obitals Multipole moments Atomic charges and electrostatic potentials Vibrational frequency IR and Raman spectra NMR properties Polarizabilities and hyperpolarizabilities Thermochemical properties Reaction pathways
1.2 Model Chemistry
1.2.1 [Gaussian98 ] PM3 HF B3LYP MP2 Hartree-Fock Becke 3 Moller-Plesset
1.2.2 Open shell Close shell :, (Restricted) R RHF, (Unrestricted) U HF UHF
1., 2. 3. 4.
1.3 Basis set LCAO-MO H 1s H 2s ψ ψ 3 ς exp( ς ) π 1s = r 5 ς r 3π 2s = r exp( ς )
Basis Sets Slater type orbitals (STO) Gaussian type orbitals (GTO) - functional form - zeroth-order Gaussian function r n n nl e r n r R ζ ζ + = 1 2 1/ 2 1/ )!] [(2 ) (2 ) ( 2 4 3 / 2 ), ( r s e r g α π α α = 2 ar c b a e z y x
Slater Gauss GTO STO STO STO GTO ( 3 6, STO-NG)
Property of Gaussian functions is that the product of two G aussians can be expressed as a single Gaussian, located alon g the line joining the centers of the two Gaussians 2 2 2 2 c mn n m n m n n m m ar r a a a a r a r a e e e e + =
STO VS. GTO
1.3.1 Minimal Basis Sets H He 1s Li Be C Ne 1s, 2s, 2px, 2py, 2pz
1.3.2 Split Valence Basis Sets H He 1s, 1s' Li Be C 1s, 2s, 2s', 2Px, 2Py, 2Pz, 2Px', 2Py', 2Pz' 3-21G 6-31G 3-21G Gauss 2 Gauss 1 Gauss
1.3.3 Polarized Basis Sets (size) (shape) 6-31G(d) 6-31G* 6-31G(d,p) 6-31G** 6-31G(d) 6-31G d 6-31G(d,p) 6-31G(d) p
1.3.4 Diffuse Functions s p 6-31+G(d) 6-31G++(d) 6-31+G(d) 6-31G(d), 6-31++G(d)
1.3.5 High Angular Momentum Basis Sets 6-31G(2d) 6-31G d 6-311++G(3df,3pd) d f p d 6-311+G(3df,2df,p) d f, d f
1.3.6 Effective Core Potential Basis Sets (Effective Core Potential, ECP) LanL2DZ
STO-3G: [H-Xe] 3-21G:[H-Xe] 6-31G(d):[H-Cl] 6-31G(d,p):[H-Cl] 6-31+G(d):[H-Cl] 6-31+G(d,p):[H-Cl] 6-311+G(d,p):[H-Br] 6-311+G(2d,p):[H-Br] 6-311+G(2df,2p):[H-Br] 6-311++G(3df,2pd):[H-Br]
1.4 * (semi-empirical) * : Hartree-Fock SCF ( ): Moller-Plesset CI QCI * (DFT)
1.4.1 AM1 PM3 MNDO Gaussian MOPAC HyperChem Spartan * * HF DFT * *
1.4.2 HF AM1,PM3,HF/6-31+G(d) MP2/ 6-311++G(2d,2p) AM1 PM3 HF MP2 R(H-F) 0.83 0.94 0.92 0.92 R(H4-F2) 2.09 1.74 1.88 1.84 R(F-F) 2.87 2.65 2.79 2.76 A(F-H4-F) 159.3 159.8 168.3 170.6 A(H3-F-F) 143.8 143.1 117.7 111.8
1.4.3 Hartree-Fock Hartree-Fock Electron Correlation( ) Fermi( ) ---- Pauli Couloub( ) ----
Electron Correlation The most significant drawback to HF theory is that it fails to adequately represent electron correlation. E corr = E NR E HF Configuration Interactions - excited states are included in the description of an electronic state Many Body Perteubation Theroy - based upon Rayleigh-Schrödinger perturbation theroy.
1.4.4 Electron Correlation and Post-SCF Methods SCF Gaussian Moller-Plesset MP2, MP3, MP4, MP5 MP2 MP3, MP4( MP4SDQ) MP2 Quadratic CI QCISD, QCISD(T), QCISD(TQ),QCISD Coupled Cluster methods ( ) ( ) CCD, CCSD, CCSD(T)
HF HF/STO-3G 73.9 HF 97.9 MP2 144.9 MP3 137.9 MP4(SDTQ) 141.8 QCISD 138.8 QCISD(T) 140.6 141.2
1.4.5 Density Functional Theory Methods DFT - Gaussian B3LYP B3PW91
1.5
6-31+G(d,p) 6-311+G(d,p)
H, He STO-3G 3-21G 6d 6-31G* 6-31G** 6-31+G(d) 6-31+G(d,p) 6-311+G(d,p) 5d